The width of a slot of a duralumin forging is (in inches) normally distributed with μ= 0.9000 and σ = 0.0030. The specification limits were given as 0.9000 ±0.0050. Show your calculations. Draw normal curves wherever appropriate.
a) What percentage of forgings will be defective?
b) What is the maximum allowable value of σ that will permit no more than 1 in 100 defectives when the widths are normally distributed with μ = 0.9000 and σ (revised value)?

Answer: To calculate the decrease in value of Samir's digger after 10000 hours, we need to determine its value at the end of each year, taking into account the yearly depreciation of 18%.

Here's the calculation for the first year:

Value at the end of Year 1 = £35950 - (£35950 * 18%) = £29576

And for the second year:

Value at the end of Year 2 = £29576 - (£29576 * 18%) = £24480.48

And so on, until we reach 10000 hours. To determine the exact value after 10000 hours, we would need to perform the calculation for each year until we reach the total number of hours used. However, this calculation would involve multiple steps and can become quite complex. A simpler way to estimate the decrease in value would be to use the concept of present value.

Answer:

He got an 80 percent.

Step-by-step explanation:

Answer:

33,000

Step-by-step explanation:

Answer:

  33.3%

Step-by-step explanation:

You want the mass volume % of a solution of 5 grams of solute in 30 grams of solution that has a density of 2 g/mL.

The volume of the solution is its mass divided by its density.

  V = m/ρ

  V = (30 g)/(2 g/mL) = 15 mL

Then the ratio of mass of solute to volume of solution is ...

  (5 g)/(15 mL) = 1/3 g/mL

Expressed as a percentage, that is ...

  (1/3 g/mL) · 100% = 33.3% mass/volume

__

Additional comment

It is usually easier to measure the volume of a liquid solution than to measure its mass. The quantity of interest in a solution is often the mass of the solute it contains, so a mass/volume ratio has a certain practicality.

The standard error represents the average deviation of the sample means from the true population mean. Rounding this value to four decimal places, the standard error of X¯¯¯ is approximtely 0.6500 mpg.

A smaller standard error indicates that the sample means are more likely to be close to the population mean.To calculate the standard error of X¯¯¯, the mean from a random sample of 25 fill-ups by one driver, we can use the formula:

Standard Error (SE) = σ / sqrt(n),

where σ is the standard deviation and n is the sample size.

In this case, the standard deviation (σ) is given as 3.25 mpg, and the sample size (n) is 25.

Plugging in these values into the formula, we have:

SE = 3.25 / sqrt(25).

Calculating the square root of 25, we get:

SE = 3.25 / 5.

Performing the division, we find:

SE ≈ 0.65.

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By using trigonometry, the missing sides are

Example 1: x = 16.7

Example 2: x = 3.2

Example 3: x = 23.5

Example 4: x = 9.3

From the question we are to determine the value of the missing sides in the given triangles

We can determine the value of the missing sides by using SOH CAH TOA

Example 1

Angle = 42°

Opposite side = x

Hypotenuse = 25

Thus,

sin (42°) = x / 25

x = 25 × sin (42°)

x = 16.7

Example 2

Angle = 75°

Opposite side = 12

Adjacent side = x

Thus,

tan (75°) = 12 / x

x = 12 / tan (75°)

x = 3.2

Example 3

Angle = 36°

Hypotenuse side = x

Adjacent side = 19

Thus,

cos (36°) = 19 / x

x = 19 / cos (36°)

x = 23.5

Example 4

Angle = 53°

Opposite side = x

Adjacent side = 7

Thus,

tan (53°) = x / 7

x = 7 × tan (53°)

x = 9.3

Hence,

The missing sides are 16.7, 3.2, 23.5 and 9.3

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The inclination of the line represented by the equation y = x + 3 is 1, and the inclination of the line represented by the equation 3x - 2y = 6 is 3/2.

To determine the inclination (or slope) of a straight line, we can examine the coefficients of the variables x and y in the equation of the line.

The inclination represents the ratio of how much y changes with respect to x.

Equation: y = x + 3

In this equation, the coefficient of x is 1, which means that for every increase of 1 in x, y also increases by 1.

This indicates that the inclination of the line is positive, meaning it slopes upwards as x increases.

Since the coefficient of x is 1, the inclination can be expressed as 1/1 or simply 1.

Equation: 3x - 2y = 6

To determine the inclination, we need to rearrange the equation in slope-intercept form (y = mx + b), where m represents the slope.

First, isolate y:

-2y = -3x + 6

Divide the entire equation by -2 to solve for y:

y = (3/2)x - 3

Now we can observe that the coefficient of x is 3/2.

This indicates that for every increase of 1 in x, y increases by 3/2. Therefore, the inclination of this line is positive, indicating an upward slope.

The inclination can be expressed as 3/2.

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The expression log₃(x²∛y²) using the laws of logarithms is 2log₃(x) + 2/3log₃(y)

From the question, we have the following parameters that can be used in our computation:

log₃(x²∛y²)

The product law of logarithms states that

log(ab) = log(a) + log(b)

Using the above as a guide, we have the following:

log₃(x²∛y²) =  log₃(x²) + log₃(∛y²)

The power law of logarithms states that

log(aᵇ) =  blog(a)

Using the above as a guide, we have the following:

log₃(x²∛y²) =  2log₃(x) + 2/3log₃(y)

This means that the values of A and B are A = 2 and B = 2/3

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Answer:

13.29 inch

Step-by-step explanation:

Given:

Square game board.

Area of square game board = 175 sq inch

To find:

The side length of the square board game.

Solution:

First of all, we need to know the formula for area of a square.

Let us have a look at the formula for area of a square.

\(Area = Side\times Side\)

OR

\(Area = Side^2\)

Putting value of area = 175 sq in and let us find the value of Side.

\(175=Side^2\\\Rightarrow Side = \sqrt{175}\\\Rightarrow Side \approx \bold{13.29\ inch}\)

Therefore, the answer is:

The appropriate side length of the square game board = 13.29 inch

Answer:

36w

Step-by-step explanation:

The fence in dead center is about 399 feet from the third base.

The Pythagorean Theorem states that in the case of a right triangle, the square of the length of the hypotenuse, which is the longest side,  is equals to the sum of the squares of the lengths of the other two sides.

Hence the equation for the theorem is given as follows:

c² = a² + b².

In which:

For the triangle in this problem, we have that:

Hence the distance is obtained as follows:

d² + 90² = 409²

\(d = \sqrt{409^2 - 90^2}\)

d = 399 ft.

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\(\huge\text{Hey there!}\)

\(\large\textsf{y = 4x - 1}\)

\(\large\text{If x= -3, then substitute it into the given equation}\)

\(\large\textsf{y = 4(-3) - 1}\)

\(\large\textsf{4(-3) = \boxed{\bf -12}}\)

\(\large\textsf{y = -12 - 1}\)

\(\large\textsf{-12 - 1 = y}\)

\(\large\textsf{-12 - 1 = \boxed{\bf -13}}\)

\(\boxed{\boxed{\large\textsf{Answer: \huge \bf y = -13}}}\huge\checkmark\)

\(\large\text{Good luck on your assignment and enjoy your day!}\)

~\(\frak{Amphitrite1040:)}\)

\( \quad \quad \quad \quad\tt{y = 4x - 1}\)

\( \quad \quad \quad \quad\tt{y = 4( - 3) - 1}\)

\( \quad \quad \quad \quad\tt{y = (- 12)- 1}\)

\( \quad \quad \quad \quad\tt{y = - 13}\)

\( \quad \quad \quad \quad \boxed{\tt \color{green}{y = - 13}}\)

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Answer:

12 + 7 = 19

19 + 10 = 29

answear = 29

Derrick and Janis together plant a total of 30 + 90 = 120 strawberry plants on the first day.

To find out how many strawberry plants Derrick and Janis planted on the first day, we need to calculate the sum of the plants they individually planted.

Derrick planted 20% of the 150 strawberry plants:

20% of 150 = (20/100) * 150 = 30 strawberry plants.

Janis planted 60% of the 150 strawberry plants:

60% of 150 = (60/100) * 150 = 90 strawberry plants.

Therefore, on the first day, Derrick and Janis planted a total of 30 + 90 = 120 strawberry plants.

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Answer:

Expanding the expression 2(d+9) gives:

2(d+9) = 2*d + 2*9

Simplifying the expression gives:

2(d+9) =2d + 18

Therefore, 2(d+9) is equivalent to 2d +18.

The simplified expression is:

Work:

To simplify this expression, I distribute 2 through the parenthesis:

\(\sf{2(d+9)}\)

\(\sf{2\cdot d + 2 \cdot9}\)

\(\sf{2d+18}\)

Volume of a cylinder = π r^2 h

Where:

r= radius = 15 in

h= heigth = 30 in

Replacing:

V = π 15^2 30 = 21,205.75 in3

The initial height of the rocket is 24 metres, the rocket hit the ground in 0.88 seconds and the height of the rocket after 4 seconds is 24 metres.

A quadratic equation is a second-order polynomial equation in a single variable x , ax²+bx+c=0. with a ≠ 0 .

The initial height of the rocket is given by the value of h when t = 0:

h(t)=-4t² + 16t + 24

h(0)=-4(0)² + 16(0) + 24

h(0)=24

So the initial height of the rocket is 24 metres.

The rocket will hit the ground when its height is 0 metres, so we can set h = 0 in the equation and solve for t:

0 = -4t²+ 16t + 24

-4t² + 16t + 24 = 0

t=-0.88 seconds

So the rocket will hit the ground after approximately 0.88 seconds.

The height of the rocket after 4 seconds is given by:

h(4)== -4(4)²+ 16(4) + 24

=-64+64+24

=24

So the height of the rocket after 4 seconds is 24 metres.

Hence, the initial height of the rocket is 24 metres, the rocket hit the ground in 0.88 seconds and the height of the rocket after 4 seconds is 24 metres.

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Answer:

the taco stand would sell 37 tacos in 1/2 an hour.

Answer:

37

Step-by-step explanation:

296 divide by 4 = 74

74 divide by 2 = 37

The necessary interventions for a patient with acute pan-creatitis who is at risk for paralytic ileus are options 1, 2, 4, and 5. Because, The common consequence of acute pan-creatitis known as paralytic ileus prevents the intestines' normal motility by inflaming the tissues around it.

(1).Provide enteral feedings: Enteral nutrients may help to encourage bowel movement.

(4).Ask if patient has passed : The passing of flatus can indicate the return of bowel function

(5).Maintain nasogastric tube : An NG tube can aid in stomach decompression and stop gastric distension.

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Answer:

One solution

Step-by-step explanation:

The only solution is x = 2/3

Answer:

3x-5=-3=19

Step-by-step explanation:

Answer:

(-2,5)

Step-by-step explanation:

\(▪▪▪▪▪▪▪▪▪▪▪▪▪ {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪\)

We know that mid - point of a line segment divides it into two equal parts, that is it divides the segment in the ratio of 1 : 1, so let's find the coordinates of the mid point of line segment joining points (-9 , 3) and (5 , 7).

let the coordinates of the points be x and y, now

Using section formula :

value of x :

value of y :

So, coordinates of the point which is midpoint of the given line is :

\( \boxed{ \boxed{ (7, 2)}}\)

The value x in the secant line using the Intersecting theorem is 4.

Intersecting secants theorem states that " If two secant line segments are drawn to a circle from an exterior point, then the product of the measures of one of secant line segment and its external secant line segment is the same or equal to the product of the measures of the other secant line segment and its external line secant segment.

From the figure:

First sectant line segment = ( x - 1 ) + 5

External line segment of the first secant line = 5

Second sectant line segment = ( x + 2 ) + 4

External line segment of the second secant line = 4

Using the Intersecting secants theorem:

5( ( x - 1 ) + 5 ) = 4( ( x + 2 ) + 4 )

Solve for x:

5( x - 1 + 5 ) = 4( x + 2 + 4 )

5( x + 4 ) = 4( x + 6 )

5x + 20 = 4x + 24

5x - 4x = 24 - 20

x = 4

Therefore, the value of x is 4.

Option C) 4 is the correct answer.

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Step-by-step explanation:

a = k/m    or       ma = k    

using 4 and 9     4* 9 = k = 36

then the equation becomes:

    ma = 36    

  using a = 6

      6 * m = 36     shows m = 6 kg

Answer:

x=\(\frac{1}{a}\)

Step-by-step explanation:

Answer:

\(\frac{a}{a} = x\)

Step-by-step explanation:

==================================================================

What we have to do is solve for x, meaning we have to get everything away from the x.

10 = 2 - 4(ax - 3)

Subtract 2 from both sides.

8 = -4(ax - 3)

Now divide by -4 from both sides.

-2 = ax - 3

Add 3 to both sides.

1 = ax

Finally, divide by a to both sides.

\(\frac{a}{a} = x\)

==================================================================

Answer:

---------------------------

There are two triangular faces with base of 16 cm and height of 15 cm and three rectangular faces.

Find the sum of areas of all five faces:

Given, vertex: (5,4) focus (-5,4).

Since the y coordinates of the vertex and the focus are the same, the focus and the vertex are on the same horizontal line, y=4. So,the axis of symmetry is a horizontal line.

SInce vertex: (5,4) and focus (-5,4), we find that the focus is at the left of the vertex. So, the parabola opens leftwards.

So, the equation of parabola is,

a=-5-(5)=-10 , since y coordinates are same.

Now, above equation becomes,

So, the equation of the parabola is,

Answer:

15. 4x¹⁰

16. 30m³

Step-by-step explanation:

15. Area of Rectangle is given by A=LW

    since W=x⁵ and L is 4 times W, L=4x⁵

    therefore, A = x⁵(4x⁵) = 4x¹⁰

16. Volume of Rectangular Prism is V=LWH

    W=6L=6m  and  H=5L=5m  and  L=m

   so V = m(6m)(5m) = 30m³

Okay, here we have this:

Considering the provided information we are going calculate how far is the plane from the airport, so we obtain the following using the law of cosines:

Finally we obtain that the plane is approximately 244 miles far from the airport.